- Return of problems pp. 59--, #53, 56, 61
- First of all, fewer than half handed it in....
- "Numerical Evidence" -- you were really supposed to dig out the ol' calculator and create a table or two, to indicate what's going on....
- #56 involves a conjecture, which we can now prove!
- #61 sets us up for today's introduction of the derivative
- You have a problem set due tomorrow (by hand).
- New assignment:
Mon 2/1 Section 2.7/3.1 - Read 3.2 in preparation for class tomorrow
- Hand in the following for grading:
pp. 106--, #69-72 (due Monday, 2/8)
- A challenge....
-
- The Intermediate Value Theorem:
- If f is a continuous function on the closed interval [a,b] and the number M satisfies f(a) < M < f(b) (note: the endpoints are not equal), there is a point c between a and b where f(c) = M.
- What can go wrong if f(a)=f(b)?
- One thing this gives us is a method for finding roots of functions to
greater and greater precision -- The Bisection Method.
- Examples:
- Preliminary questions, p. 86: 1, 2, 4
- #7, p. 86
- #15, p. 86
- #24, p. 87
- "time, position, velocity"
- If we have the record of the position, could we recover the velocity?
- If we have the record of the velocity, could we recover the position?
- Secant
lines approximating tangent lines....
- The definition:
- Example problems:
- #5, p. 103
- #21, p. 104
- #26, p. 104
- #49, p. 105